Updated July 23, 2023
To get to a safari in Ngorongoro National Park, Tanzania, the friend of an LVA staffer flew into Dar Es Salaam. She related that after clearing customs, she and the other arriving international passengers were besieged by taxi drivers who latched onto their luggage and didn't let go, triggering a sudden desperate tug of war over suitcases, carry-ons, purses, and the like. An unfortunate few lost the struggle with the cabbies; with control of the luggage, the drivers essentially held it hostage and the passengers were at their mercy.
This is an admittedly extreme example, but varying degrees of this scenario are played out all over the world. The point is that no one -- other than TSA agents at airport security checks, customs officials, and other government authorities -- can or should handle your luggage without your express consent. It's not only not inappropriate to refuse luggage service from bellmen, it's perfectly acceptable and happens all the time.
If you're planning on handling your own luggage, when disembarking from a taxi, limo, airport shuttle, or bus in front of a hotel or airport, take charge of your luggage immediately and dismiss the luggage handler(s) with a simple, "Thanks anyway; I'm good," or "I always handle the luggage myself." Baggage personnel differ in terms of aggressiveness, but a firm "No thank you" always discourages all but the most Tanzanian-like hustlers.
Keep in mind that baggage handling, along with valet parking, housekeeping, and table waiting, is a service provided by hospitality establishments for the comfort and convenience of their guests. Tipping is customary (in the U.S.) and cash gratuities are expected for good service, but they're not mandatory. Don't tip and you'll be considered a stiff, but there are -- or at least should be -- no other consequences.